University of Jordan
Faculty of Engineering and Technology
Electrical Engineering Department
Electronics Lab EE 204
Explanation of Experiment 2
Network Theorems of DC Circuits
Superposition theorem:
The strategy used in the Superposition Theorem is to eliminate all but one source of power
within a network at a time, using series/parallel analysis to determine voltage drops (and/or
currents) within the modified network for each power source separately. Then, once voltage
drops and/or currents have been determined for each power source working separately, the
values are all “superimposed” on top of each other (added algebraically) to find the actual
voltage drops/currents with all sources active.
In superposition; eliminating a voltage source means to replace the source with a short
circuit, Where eliminating a current source means to replace it with an open circuit. see the
figure below:
part
of
1st
superposition:
keep the voltage
source(E)
and
replace
the
current
source
with an open
circuit, and find the requirements(I1′,I2′,I3′,V1′,V2′,V3′).
2nd part :reconnect the current source and replace the voltage source with a short circuit, find
the requirements(I1″,I2″,I3″,V1″,V2″,V3″).
Eng. Ala’a Alshubbak, Eng. Zienab Hyari
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Then the values are all “superimposed” on top of each other (added algebraically) to find the
actual voltage drops/currents with all sources active, Where:
V1=V1′+V1″
V2=V2′+V2″
V3=V3′+V3″
I1=I1′+I1″
I2=I2′+I2″
I3=I3′+I3″
Note : take into consideration the directions of each value.
Thevenin’s theorem:
Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how
complex, to an equivalent circuit with just a single voltage source and series resistance
connected to a load. The qualification of “linear” is identical to that found in the
Superposition Theorem, where all the underlying equations must be linear (no exponents or
roots). If we're dealing with passive components (such as resistors, inductors and capacitors),
this is true.
Thevenin's Theorem is especially useful in analyzing power systems and other circuits where
one particular resistor in the circuit (called the “load” resistor) is subject to change, and recalculation of the circuit is necessary with each trial value of load resistance, to determine
voltage across it and current through it.
Thevenin's Theorem makes this easy by temporarily removing the load resistance from the
original circuit and reducing what's left to an equivalent circuit composed of a single voltage
source and series resistance. The load resistance can then be re-connected to this “Thevenin
equivalent circuit” and calculations carried out as if the whole network were nothing but a
simple series circuit:
Eng. Ala’a Alshubbak, Eng. Zienab Hyari
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The “Thevenin Equivalent Circuit” is the electrical equivalent of B1, R1, R3, and B2 as seen
from the two points where our load resistor (R2) connects.
The Thevenin equivalent circuit, if correctly derived, will behave exactly the same as the
original circuit formed by B1, R1, R3, and B2. In other words, the load resistor (R2) voltage
and current should be exactly the same for the same value of load resistance in the two
circuits. The load resistor R2 cannot “tell the difference” between the original network of B1,
R1, R3, and B2, and the Thevenin equivalent circuit of EThevenin, and RThevenin, provided that the
values for EThevenin and RThevenin have been calculated correctly.
The advantage in performing the “Thevenin conversion” to the simpler circuit, of course, is
that it makes load voltage and load current so much easier to solve than in the original
network. Calculating the equivalent Thevenin source voltage and series resistance is actually
quite easy. First, the chosen load resistor is removed from the original circuit, replaced with a
break (open circuit):
Next, the voltage between the two points where the load resistor used to be attached is
determined(VThevenin). Use whatever analysis methods are at your disposal to do this. In this
case, the original circuit with the load resistor removed is nothing more than a simple series
circuit with opposing batteries, and so we can determine the voltage across the open load
terminals by applying the rules of series circuits, Ohm's Law, and Kirchhoff's Voltage Law,
this voltage is called Thevenin equivalent voltage .
Then remove the sources ;same as superposition ( voltage source is replaced by a short
circuit, and current source is replaced by an open circuit ) for which you can find the
equivalent R (RThevenin)
Eng. Ala’a Alshubbak, Eng. Zienab Hyari
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Finally the equivalent Thevenin circuit is:
Norton theorem:
Norton's Theorem states that it is possible to simplify any linear circuit, no matter how
complex, to an equivalent circuit with just a single current source and parallel resistance
connected to a load. Just as with Thevenin's Theorem, the qualification of “linear” is identical
to that found in the Superposition Theorem: all underlying equations must be linear (no
exponents or roots).
Contrasting our original circuit against the Norton equivalent:
remember that a current source is a component whose job is to provide a constant amount of
current, outputting as much or as little voltage necessary to maintain that constant current.
As with Thevenin's Theorem, everything in the original circuit except the load resistance has
been reduced to an equivalent circuit that is simpler to analyze. Also similar to Thevenin's
Theorem are the steps used in Norton's Theorem to calculate the Norton source current
(INorton) and Norton resistance (RNorton).
As before, the first step is to identify the load resistance and remove it from the original
circuit,Then, to find the Norton current (for the current source in the Norton equivalent
circuit), place a direct wire (short) connection between the load points and determine the
Eng. Ala’a Alshubbak, Eng. Zienab Hyari
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resultant current. Note that this step is exactly opposite the respective step in Thevenin's
Theorem, where we replaced the load resistor with a break (open circuit):
To calculate the Norton resistance (RNorton), we do the exact same thing as we did for
calculating Thevenin resistance (RThevenin)
Now our Norton equivalent circuit looks like this:
Eng. Ala’a Alshubbak, Eng. Zienab Hyari
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